BentRay-NeRF: Bent-Ray Neural Radiance Fields for Robust Speed-of-Sound Imaging in Ultrasound Computed Tomography

Ultrasound computed tomography (USCT) is a promising technique for breast cancer detection because of its quantitative imaging capability of the speed of sound (SOS) of soft tissues and the fact that malignant breast lesions often have a higher SOS compared to healthy tissues in the human breast. Compared to waveform inversion-based USCT, bent-ray tracing USCT is relatively less computationally expensive, which particularly suits breast cancer screening in a large population. However, SOS image reconstruction using bent-ray tracing in USCT is a highly ill-conditioned problem, making it susceptible to measurement errors. This presents significant challenges in achieving stable and high-quality reconstructions. In this study, we show that using implicit neural representation (INR), the ill-conditioned problem can be well mitigated, and stable reconstruction is achievable. This INR approach uses a multilayer perceptron (MLP) with hash encoding to model the slowness map as a continuous function, to better regularize the inverse problem and has been shown more effective than classical approaches of solely adding regularization terms in the loss function. Thereby, we propose the bent-ray neural radiance fields (BentRay-NeRF) method for SOS image reconstruction to address the aforementioned challenges in classical SOS image reconstruction methods, such as the Gauss-Newton method. In silico and in vitro experiments showed that BentRay-NeRF has remarkably improved performance compared to the classical method in many aspects, including the image quality and the robustness of the inversion to different acquisition settings in the presence of measurement errors.